Doku Anomalisi İçeren Beyin MR İmgeleri Üzerinde Mumford- Shah Tabanlı Bölütleme / Mumford-Shah Based Segmentation of Brain MR Images With Tissue Abnormalities

Bu çalışmada imge bölütleme problemi Mumford-Shah enerji enazlama problemi şeklinde ifade edilmiş, problemin çözümü için getirilen öneriler incelenmiş ve seçilen çözüm yöntemi uygulanıp, algoritma, doku anomalileri içeren örnek beyin manyetik rezonans (MR) imgeleri üzerinde değerlendirilmiştir. Uygulamalarda kullanılan örnek imgeler, beyin tümörüne bağlı ödem oluşumu ve multiple sclerosis (MS) lezyonları bulunduran imgeler arasından seçilmiştir. Elde edilen sonuçlar her iki durum için de sayısal ve görsel olarak sunulmuş, sonuçlar niteliksel ve niceliksel anlamda değerlendirilmiştir. Abstract In this study, image segmentation problem is expressed in terms of Mumford-Shah energy minimization problem, several solution proposals for the problem are investigated, chosen method of solution is implemented, and the algorithm is evaluated using brain magnetic resonans (MR) images which contain tissue abnormalities. Sample images used in the experiments are chosen among the ones which contain oedema formation due to brain tumor, and multiple sclerosis (MS) lesions. Gathered results are presented in both visual and numerical forms for both cases, results are evaluated qualitatively and quantitatively.

Anahtar Kelimeler:

-

PDF

___

1] Mumford, D. and Shah, J., "Optimal approximations by piecewise smooth functions and associated variational problems," Communications on Pure and Applied Mathematics, vol. 42, no. 5, pp. 577--685, 1989.
[2] Zhou, J., Shu, H., Xia, T., Luo, L., "PET Image Reconstruction Using Mumford-Shah Regularization Coupled with L1 Data Fitting," Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the , vol., no., pp.1905-1908, 17-18 Jan. 2006
[3] Lin, P., Yan, X., Zheng, C., Yang, Y., "Medical image segmentation based on Mumford-Shah model," Communications, Circuits and Systems, 2004. ICCCAS 2004. 2004 International Conference on , vol.2, no., pp. 942- 945 Vol.2, 27-29 June 2004
[4] Du, X., Bui, T.D., "Image segmentation based on the Mumford-Shah model and its variations," Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on , vol., no., pp.109-112, 14-17 May 2008
[5] Lam, B.S.Y., Yan, H., "Blood Vessel Extraction Based on Mumford Shah Model and Skeletonization," Machine Learning and Cybernetics, 2006 International Conference on , vol., no., pp.4227-4232, 13-16 Aug. 2006
6] Geman, S. and Geman, D., "Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images," Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. PAMI-6, no. 6, pp. 721 -741, 1984.
[7] Cremers, D., Tischhauser, F., Weickert, J. and Schnorr, C., "Diffusion snakes: introducing statistical shape knowledge into the Mumford-Shah functional," J. OF COMPUTER VISION, vol. 50, 2002.
[8] Vese, L.A. and Chan, T.F., "A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model," International Journal of Computer Vision, vol. 50, pp. 271-293, 2002.
[9] Grady, L. and Alvino, C., Reformulating and Optimizing the Mumford-Shah Functional on a Graph - A Faster, Lower Energy Solution.: Springer Berlin / Heidelberg, vol. 5302, pp. 248-261, 2008.
[10] Pock, T., Chambolle, A., Cremers, D. and Bischof, H., "A convex relaxation approach for computing minimal partitions," in Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pp. 810 -817, june 2009.
[11] Chambolle, A., "Finite-differences discretizations of the mumford-shah functional," M2AN, vol. 33, no. 2, pp. 261-288, 1999
[12] Tortorelli, V.M. and Ambrosio, L., "Approximation of functional depending on jumps by elliptic functional via t-convergence," Communications on Pure and Applied Mathematics, vol. 999-1036, p. 43, 1990.
[13] Erdem, E., Sancar-Yilmaz, A. and Tari, S., "MumfordShah regularizer with spatial coherence," in Proceedings of the 1st international conference on Scale space and variational methods in computer vision, Berlin, Heidelberg, pp. 545--555, 2007.
[14] Cheng, A. and Cheng D. T., “Heritage and early history of the boundary element method”, Engineering Analysis with Boundary Elements, 29, 268–302. 2005